Despite some people opining about how email is broken, the fact is that people prefer its simplicity and universal access.
As a team lead I tried to start us on Asana which I use for personal projects and I think is a fantastic product. I assumed people would love it. To my surprise only a few actually signed up (reluctantly) and after two weeks the project was completely silent and people were emailing to ask questions or check for updates that I had already submitted to the Asana project. After asking them to check the project enough times I gave up and switched back to email.
Couldn't you replace social network and project management tool with search engine and email app?
How big of a market are the "zero inbox zealots"?
One of Mailbox App's pitch points is even along these lines: "Inbox zero. Daily.".
My main problem is that with my style of thinking, I'll get an email that will make me think, "Yeah, I want to do something about that... later." But not "later" in terms of a calendar date - "later" in terms of when I am enabled to work on it, as in when a blocking dependency disappears. I can't find an easy way to make those emails disappear until they are triggered by me completing other things I care about.